Llandaff
Thursday evening. November 9
My dear Father.
I send you a neat proof of the theorem. That if you join the angles of a triangle to the points of bisection of the opposite sides there [sic] lines meet in a point; proved by the doctrine of limits.
[illustration]
In the first place I assume, that if a rectilineal figure becomes indefinitely small it may be considered as a mathematical point
Now let A B C be a triangle and D.E F the centres of its sides.
If D E. & .D F be joined
D.E C F is a parallelogram. & ˆ D C bisects the other diagonal E F. in H
Similarly, B F bisects D E in C
and, A E bisects D F in K.
ˆ the 3 lines from the angles to the centres of sides of the large triangle are reduced to 3 lines from the centres of sides to the angles angles of the small triangle
The same holds in the case of the still smaller triangle, G H K. & for each successive triangle which can be inscribed in the preceding.
ˆ it is true in the limit when the no of inscribed ∆ s is infinite but the ∆ s are then indefinitely small & become a mathematical point.
ˆ these 3 lines pass through one point.
Q. E D.
I examined Tintern Abbey 1 carefully and made out the arrangement without difficulty.
Please cite as “TALBOT8893,” in Ɛpsilon: accessed on